Combine all the ingredients except the rum in a small saucepan and cook over medium-low heat, whisking constantly, until the sauce has thickened and coats the back of a spoon, about 10 minutes. Do not allow the sauce to boil or the egg will curdle and the sauce will not be smooth. (If this does happen, then simply strain through a fine-mesh sieve.) Remove from the heat, stir in the rum, and set aside to cool slightly.
Makes about 2 cups